Origin of the Photoinduced Geometrical Change of Copper(I) Complexes from the Quantum Chemical Topology View

Copper(I) complexes (CICs) are of great interest due to their applications as redox mediators and molecular switches. CICs present drastic geometrical change in their excited states, which interferes with their luminescence properties. The photophysical process has been extensively studied by several time-resolved methods to gain an understanding of the dynamics and mechanism of the torsion, which has been explained in terms of a Jahn–Teller effect. Here, we propose an alternative explanation for the photoinduced structural change of CICs, based on electron density redistribution. After photoexcitation of a CIC (S₀→S₁), a metal-to-ligand charge transfer stabilizes the ligand and destabilizes the metal. A subsequent electron transfer, through an intersystem crossing process, followed by an internal conversion (S₁→T₂→T₁), intensifies the energetic differences between the metal and ligand within the complex. The energy profile of each state is the result of the balance between metal and ligand energy changes. The loss of electrons originates an increase in the attractive potential energy within the copper basin, which is not compensated by the associated reduction of the repulsive atomic potential. To counterbalance the atomic destabilization, the valence shell of the copper center is polarized (defined by ∇²ρ(r) and ∇²V_ne(r)) during the deactivation path. This polarization increases the magnitude of the intra-atomic nuclear–electron interactions within the copper atom and provokes the flattening of the structure to obtain the geometry with the maximum interaction between the charge depletions of the metal and the charge concentrations of the ligand.     

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Synthesis and Characterization of a New Metal-organic Framework with Nou Topology

A new compound, [H2N(CH3)2]2[Zn(btec)].H2O(1, H4 btec = 1,2,4,5-benzenetetracarboxylic acid) has been solvothermally synthesized and structurally characterized by singlecrystal X-ray diffraction. The crystal structure is of monoclinic, space group P21/c with a = 9.5741(3), b = 14.5044(4), c = 13.7329(5) , β = 100.582(4)°, V = 1874.61(10) 3, C14H20N2O9 Zn, Mr = 425.7, Z = 4, Dc = 1.387 g/cm3, μ = 1.349 mm-1, F(000) = 776, R = 0.0560 and w R = 0.1684 for 2834 observed reflections(I 2σ(I)). Compound 1 based on μ4-btec and tetrahedral building unit features a three-dimensional(3D) anionic framework with mixed connected nou topology. The luminescent property and thermogravimetric analysis of compound 1 are investigated.